Journal of Mathematical Biology

, Volume 66, Issue 1–2, pp 399–420 | Cite as

Orthology relations, symbolic ultrametrics, and cographs

  • Marc Hellmuth
  • Maribel Hernandez-Rosales
  • Katharina T. Huber
  • Vincent Moulton
  • Peter F. Stadler
  • Nicolas Wieseke


Orthology detection is an important problem in comparative and evolutionary genomics and, consequently, a variety of orthology detection methods have been devised in recent years. Although many of these methods are dependent on generating gene and/or species trees, it has been shown that orthology can be estimated at acceptable levels of accuracy without having to infer gene trees and/or reconciling gene trees with species trees. Thus, it is of interest to understand how much information about the gene tree, the species tree, and their reconciliation is already contained in the orthology relation on the underlying set of genes. Here we shall show that a result by Böcker and Dress concerning symbolic ultrametrics, and subsequent algorithmic results by Semple and Steel for processing these structures can throw a considerable amount of light on this problem. More specifically, building upon these authors’ results, we present some new characterizations for symbolic ultrametrics and new algorithms for recovering the associated trees, with an emphasis on how these algorithms could be potentially extended to deal with arbitrary orthology relations. In so doing we shall also show that, somewhat surprisingly, symbolic ultrametrics are very closely related to cographs, graphs that do not contain an induced path on any subset of four vertices. We conclude with a discussion on how our results might be applied in practice to orthology detection.


Orthology Symbolic ultrametric Cograph Cotree Rooted triples 

Mathematics Subject Classification

05C05 92D15 68R10 


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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Marc Hellmuth
    • 1
  • Maribel Hernandez-Rosales
    • 2
    • 3
  • Katharina T. Huber
    • 4
  • Vincent Moulton
    • 4
  • Peter F. Stadler
    • 2
    • 3
    • 5
    • 6
    • 7
  • Nicolas Wieseke
    • 3
    • 8
  1. 1.Center for BioinformaticsSaarland UniversitySaarbrückenGermany
  2. 2.Max-Planck-Institute for Mathematics in the SciencesLeipzigGermany
  3. 3.Interdisciplinary Center of BioinformaticsUniversity of LeipzigLeipzigGermany
  4. 4.School of Computing SciencesUniversity of East AngliaNorwichUK
  5. 5.Bioinformatics Group, Department of Computer ScienceUniversity of LeipzigLeipzigGermany
  6. 6.Institute for Theoretical ChemistryUniversity of ViennaViennaAustria
  7. 7.Santa Fe InstituteSanta FeUSA
  8. 8.Parallel Computing and Complex Systems Group, Department of Computer ScienceUniversity of LeipzigLeipzigGermany

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